In this article, he discusses the concept of missing a shot “thin”, here’s his diagram and description:

Here’s a tough situation; both of you are shooting the eight ball, and you have a tough cut. Some of the pros say that if you have to miss the shot, miss it too thin (the light green line here), rather than too thick (red line). The reason is that after the cue ball has gone back up table, you haven’t sold the farm when you miss.

In most of the discussions I’ve seen about “missing on the pro side”, the object ball (8-ball here) is closer to the short rail than it is to the long rail. When this is the case it’s easier to make the ball on the “non-pro” side – you have a better chance if you undercut it:

I’m using the same layout here, but showing shot-paths that “miss by less”. You can see that the angle of approach is equal for both balls (relative to the pocket – see the black centerline) , however the undercut shot (red line) produces a gentler, obtuse angle of reflection, allowing softly hit shots to be pocketed in off the jaws of the pocket. The angle of reflection for the green line is acute, if you miss you miss.

So it’s a compromise: you have a better chance of making a shot with on the “non-pro” side, but if you do miss, you will probably leave your opponent an easier shot. Pool is filled with these trade-offs, the longer you play the more you discover subtleties like this, which can drive you crazy but also keep you interested.